Question: Simplify the following expression: $ z = \dfrac{p + 3}{-6p} - \dfrac{-7}{4} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{p + 3}{-6p} \times \dfrac{4}{4} = \dfrac{4p + 12}{-24p} $ Multiply the second expression by $\dfrac{-6p}{-6p}$ $ \dfrac{-7}{4} \times \dfrac{-6p}{-6p} = \dfrac{42p}{-24p} $ Therefore $ z = \dfrac{4p + 12}{-24p} - \dfrac{42p}{-24p} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{4p + 12 - 42p }{-24p} $ Distribute the negative sign: $z = \dfrac{4p + 12 - 42p}{-24p}$ $z = \dfrac{-38p + 12}{-24p}$ Simplify the expression by dividing the numerator and denominator by -2: $z = \dfrac{19p - 6}{12p}$